Question: Assume this first statement is true: If I study really hard, I will ace the test. Logically, can you deduce that this second statement must be true from the first one? If I did not ace the test, then I did not study really hard.
Answer: Is the second statement the converse, inverse, or contrapositive of the original statement? The second statement is the contrapositive of the original statement. The contrapositive is logically equivalent to the original statement, so yes, the second statement can be deduced from the first statement.